1 February 2023 A generalization of Rasmussen’s invariant, with applications to surfaces in some four-manifolds
Ciprian Manolescu, Marco Marengon, Sucharit Sarkar, Michael Willis
Author Affiliations +
Duke Math. J. 172(2): 231-311 (1 February 2023). DOI: 10.1215/00127094-2022-0039

Abstract

We extend the definition of Khovanov–Lee homology to links in connected sums of S1×S2’s and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in S1×S2, we compute the invariant by reinterpreting it in terms of Hochschild homology. As applications, we prove inequalities relating the Rasmussen-type invariant to the genus of surfaces with boundary in the following 4-manifolds: B2×S2, S1×B3, CP2, and various connected sums and boundary sums of these. We deduce that Rasmussen’s invariant also gives genus bounds for surfaces inside homotopy 4-balls obtained from B4 by Gluck twists. Therefore, it cannot be used to prove that such homotopy 4-balls are nonstandard.

Citation

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Ciprian Manolescu. Marco Marengon. Sucharit Sarkar. Michael Willis. "A generalization of Rasmussen’s invariant, with applications to surfaces in some four-manifolds." Duke Math. J. 172 (2) 231 - 311, 1 February 2023. https://doi.org/10.1215/00127094-2022-0039

Information

Received: 22 December 2020; Revised: 22 November 2021; Published: 1 February 2023
First available in Project Euclid: 5 January 2023

MathSciNet: MR4541332
Digital Object Identifier: 10.1215/00127094-2022-0039

Subjects:
Primary: 57K18
Secondary: 57K40

Keywords: Gluck twist , Hochschild homology , Khovanov homology , slice genus

Rights: Copyright © 2023 Duke University Press

Vol.172 • No. 2 • 1 February 2023
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